Complementary Graphs and Edge Chromatic Numbers
β Scribed by Alavi, Y.; Behzad, M.
- Book ID
- 118190790
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 1971
- Tongue
- English
- Weight
- 233 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0036-1399
- DOI
- 10.1137/0120020
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π SIMILAR VOLUMES
## Abstract Given a simple plane graph __G__, an edgeβface __k__βcoloring of __G__ is a function Ο : __E__(__G__) βͺ __F__(G)βββ {1,β¦,__k__} such that, for any two adjacent or incident elements __a__, __b__ β __E__(__G__) βͺ __F__(__G__), Ο(__a__)ββ βΟ(__b__). Let Ο~e~(__G__), Ο~ef~(__G__), and Ξ(__G_
For any simple graph G, Vizing's Theorem [5] implies that A (G)~)((G)<~ A(G)+ 1, where A (G) is the maximum degree of a vertex in G and x(G) is the edge chromatic number. It is of course possible to add edges to G without changing its edge chromatic number. Any graph G is a spanning subgraph of an e
## Abstract A proper edge coloring of a graph __G__ is called acyclic if there is no 2βcolored cycle in __G__. The acyclic edge chromatic number of __G__, denoted by Ο(__G__), is the least number of colors in an acyclic edge coloring of __G__. In this paper, we determine completely the acyclic edge